WPMAT
CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority.
This work was funded by the RCUK Energy Programme [grant number EP/I501045] .
Nano-cluster defects in W&W alloys:
Uncertainty quantification assessment
from multi-scale modelling
Duc Nguyen-Manh
Culham Centre of Fusion Energy, UKAEA
Supported by EuroFusion, FP7 and IFERC-CSC projects
Collaborators: F. Hofmann, D. Mason, J. Wrobel, S. Dudarev
IAEA Technical Meeting CCN4, Vienna, 29-31 July 2015
WPMATMulti-scale materials modelling
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Slide 1
DNM, Bratkovsky, Pettifor, Phil. Trans. Roy. Soc. Lond. ,315 (1995) 529
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2
DFT -> Interatomic potentials -> plastic deformation
WPMATMicrostructures in irradiated materials
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Slide 3
S.J, Zinkle and L.L. Snead, Annu. Rev. Mater. Res. , 44, 241 (2014)
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Transmutation effect under neutron irradiation
4
WPMATIntegrated modelling of fusion power-plant
Systematic ab-initio data base of defect energetics
Using the available ab-initio modelling methods for modelling the degree of de-
cohesion at grain boundaries due to helium accumulation, and combining it with
neutron transport and transmutation rate analysis for evaluating the rate of helium
accumulation in an integrated multi-scale study of neutron-induced dpa,
transmutations, gas production, helium embrittlement of fusion materials.
M.R. Gilbert, S.L. Dudarev, DNM, S. Zheng, L.W. Packer, J.C. Sublet JNM 442 (2013), S755-S760
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• Systematic assessment from electronic level
• He clusters trapping by noble-gas impurities in W
vs. TDS measurements
• Lattice swelling & modulus changes in irradiated
W: XRMD & SAW vs. MM
• Nano-clusters of vacancies vs. TEM of high-
temperature annealing irradiated W
• Anomalous precipitation in self-ion irradiated W-
Re alloys vs. APT experiments
OUTLINE
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Slide 6
WPMATIntegrated view of materials in DEMO fusion
Divertor’s function is to extract heat, He ash and impurities from plasma
WPMATElectronic level: challenge with bcc TMs & alloys
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Slide 8
DNM, D.G. Pettifor, V. Vitek, PRL, 85, 4136 (2000)
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Systematic studies of electronic structure (group 5B vs. 6B)
effects for radiation damage
9
WPMATCrowdion motion: Frenkel-Kontorova model
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Slide 10
WPMATMigration barriers of crowdion
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Slide 11
Analytic solutions: S.P. Fitzgerald, DNM, PRL, 101 (2008) 115504
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In situ TEM observation of 1D nanometer-size SIA loops
12Science, 318, 9th Nov. 2007
WPMATNoble-gas ion implantation to simulate neutron-
induced damage
•Fast neutrons lead to the formation of large amount of He and H via the nuclear transmutation reactions giving rise to radiation swelling and grain boundary embrittlement. So far, most of investigation has been focused on He atoms behaviour in the radiation environment of fusion reactor systems
•Multi-beam ion implantation experiments promote new ideas to consider He co-implanting with other inert-gas ions (Ne, Ar, Kr, Xe) to simultaneously get dpa damage and dissolved noble gases. A question arises as to whether inert-gas atoms would be a good analogue for He?
•The effect of inert gases incorporation in bcc transition metals has not been systematically studied even though the agglomeration of noble gas atoms is important in understanding swelling in fission reaction (Xe atoms are is produced in the reaction with uranium and trend to coalesce into bubbles in uranium dioxide). Traditional view is that there is a similarity between He and other inter-gas atoms because of no chemical interactions and only local distortion increases from He to Ne, Ar, Kr, Xe.
JANNuS platform: Ion-beam simulation of materials science (Y. Serruys et al.)
WPMATThermal Desorption Spectra in bcc-W :
Interaction of injected He with lattice defects
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Slide 14
E.V. Kornelsen, Rad. Effects, vol. 13 (1972) 227
• He injected into W as 250 eV ions does not itself produce any observable damage
• But He is trapped in that created the prior heavy ion bombardment (Kr, for example)
• TDS shows that He is bound with several discrete energies
• Correlation of binding states with temperature, He doses and the mass of damaging ions
WPMATNoble-gas vacancy binding energy trend:
Systematic study of electronic structure effects
For noble-gas elements in bcc-W: DNM, S.L. Dudarev, NIMB, 352 (2015) 86-91
WPMATPartial DOS for inert-gas (IG) impurities in W:
role of p-electrons in IG-v binding energies
WPMATTrapping of a Helium atom by inert-gas defects:
Difference between DFT and Experimental data is small
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Slide 17
DNM, S.L. Dudarev, NIMB 352 (2015) 86
Experimental data are taken from LANDOLT-BORNSTEIN, vol. 25 (1991)
DFT EXP
4.63 4.6
3.11 3.1
2.47 2.3
1.93 1.9
1.66 1.5
1.24 1.2
WPMATExperimental validation:
Thermal desorption spectrometryAttachment of He atom to 5 impurity traps: HeV, Ne, Ar, Kr, Xe in bcc-W
E.V. Kornelsen and A.A. Van Gorkum, JNM, 92 (1980) 79
WPMATDissociation energy of a He trapped
by (n-1)He-IG-v clusters in bcc-W
DNM, S.L. Dudarev, Nuc. Ins. Meth. B 352 (2015) 86
WPMATExperimental measurement of lattice swelling and
modulus change under irradiation vs. MM validation
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Slide 20
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Measurements of elastic properties and lattice swelling
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Slide 21
3100 apmm He implanted
WPMATFrom continuum elasticity to atomic-level stresses
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Slide 22
WPMATUQ: From DFT to Experimental Data
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Slide 23
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Micro-structural evolution in W&W alloys under irradiation
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Slide 24
Evidence of vacancy
loops in irradiated
tungsten (2 MeV
W+, T = 300°C,
1014 W+/cm2)
Xiaoou Yi (2004)
High-temperature
recovery in W after
neutron irradiation
(Stage IV and V ???)
L.K. Keys et al. Phys.
Rev. 176 (1968) 851
Vacancy clusters
& He-vac interaction
and W, Fe & Fe
alloys (PAS, NRA, TEM)
M-F Barthe et al. ,
May 26th 2015
� Micro-structural
evolution associate with
Formation of vacancy
cluster, stable
configurations, binding
energies, activation
energies of transition,
migration process at
high temperature
WPMATNeutron irradiation in Tungsten
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Slide 25
WPMATSIA loops loss and void formation at high temperature
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Slide 26
F. Ferroni, Acta Mat. 90 (2015) 380; Isothermal and isochronal annealing of
2MeV irradiated W, 500C-1200C, 10^14 W+/cm2
WPMAT
• An apparent inability of DFT within LDA and GGA to describe vacancy
formation energy accurately not only in bcc metals (recent DFT data
3.0-3.3 eV w.r.t cell sizes, k-points Jwhereas experimental values are
3.5-4.0 eV in bcc-W) but also in fcc metals such as AlJ
• Theoretical treatment of electronic surfaces – i.e., strongly
inhomogeneous electron density is the weakness of popular functionals.
Surface effects for exchange & correlation (XC)
energies in first-principles modelling
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Slide 27
L. Vitos et al., PRB 62 (2000) 10046;
R. Armiento, A.E. Mattsson, PRB, 72
(2005) 065108 (AM05): treatment
of electron gas at surface and interior
Region. Could AM05 be better than
LDA and PBE for solids (J. Chem.
Phys. 128 (2008) 084714?
Density parameter: electron radius r_s
WPMATAM05 calculations for vacancy clusters
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Slide 28
� M. Muzyk, DNM, K.J. Kurzydlowski, N.L. Baluc, S.L. Dudarev, PRB, 84, 104115
(2011)� Cross checking empirical potentials calculations (Ref. 71) T. Ahlgren et al. JAP 107(2010) 033516� DFT predicted a
lower energy 5-vacancy cluster configuration
• l. Ventelon et al. JNM 425 (2012) 16: SIA and di-vacancy in bcc TMs
• D. Kato et al., Nov. 2014 IAEA-ICTP Conference: Multiple H trapping by vacancies in W
WPMAT
• The potential has been re-fitted to better reproduce known
vacancy clusters (1-6) in tungsten. In particular it reproduces
surface energies and small vacancy clusters (di-vacancy and
tri-vacancy) reasonably well in a comparison with DFT data.
• The AT embedding functional is corrected at the low electron
density region
• Electron, phonon entropies and thermal conductivity at finite T
are investigated by D. Mason
• Repulsive pair potentials are also modified to avoid
discontinuous second derivatives (fitted to higher-order
polynomials)
Surface effects implemented in corrected
Ackland-Thetford (AT) potentials for bcc-W
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Slide 29
WPMATCorrected AT potential prediction for nano-cluster of vacancies
Slide 30
Presentation title / date
• Number of different possible
configuration (M) that number of
vacancies (n) can be arranged in N
lattice positions increases for large
cluster: M=N*(N-1)*…(N-n+1)/n
• The procedure to generate
vacancy cluster is based on a
simulated annealing search
• DFT calculations were performed
for vacancy cluster configurations
generated by corrected AT
potentials
WPMATFormation energies for 1-10 vacancy clusters in bcc-W
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Slide 31
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Low-energy configuration prediction (1-15)
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For 15-vacancy cluster, the <110> facetted dodecahedral configuration is the most stable one
WPMATVacancy nano-clusters stability
from electronic structure calculations
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Slide 33
8v1: 23.426 eV (DFT) 23.429 eV (Corr-AT); 8v2: 22.958 eV (DFT) 23.467 eV (Corr-AT)
WPMATSurface effect of formation energies
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Slide 34
WPMATVolume relaxation of vacancy clusters
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Slide 35
Importance of defect
volume relaxation in
understanding of
swelling effect in He-
implanted tungsten
from multi-
scale modelling
F. Hofmann, DNM,
M. Gilbert, C.E Beck, J.K.
Eliason, A.A. Maznev, W.
Liu, D. Armstrong, K.A.
Nelson, S.L. Dudarev
Acta Mat. 89 (2015) 352
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Migration energies: DFT vs. corrected AT
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Slide 36
WPMAT
Tri-vacancy configuration changes
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Slide 37
3v1 configuration has the lowest migration energy (DFT: 1.15 eV, corrected AT: 1.46 eV).
This tri-vacancy can migrate without dissociation and changing its shape
WPMATMigration of tri-vacancy cluster without dissociation
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Slide 38
“Monkey” saddle point configuration of tri-vacancy cluster from DFT prediction
WPMATTransferable of new W potentials into W-He system
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Slide 39
A. De Backer et al. (2015), unpublished
WPMATVacancy clusters: EAM-W vs. DFT
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Slide 40
WPMATKMC simulation of vacancy cluster dissociation
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Slide 41
4-vacancy clusters 9-vacancy clusters
First frame is after 50 of kmc steps, corresponding to 240 first order moves, 42ms real time.
At frame 29, (10807 1st order moves, 2126ms) a vacancy splits off the cluster.
At frame 37 the monovac has found the cluster again, and at frame 45 it is off again.
Dissociation time is found from frame 29, the first time cluster does not immediately reform.
WPMATDissociation times and temperatures
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Slide 42
• Mean inverse dissociation rate for fixed cluster sizes and temperature
• Characteristic temperature at which dissociation rate = 1/s from Arrhenius plot
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Effect of elastic relaxation
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Slide 43
WPMATIon-irradiation-induced clustering in W-Re, W-Re-Os
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Slide 44
A. Xu et al., Acta Mat. 87 (2015) 121, APT and nano-indentation measurements
of 33 dpa irradiation at 573K and 773K
WPMATUn-irradiated vs. irradiated W-Re and W-Re-Os alloys
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Slide 45
L. Romaner et al., PRL (2010): Effect of Re on dislocation core structure in W
WPMATMethods: Genetic algorithms to predict clustering from
solute/point-defect interactions based on QM Hamiltonian
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Slide 46
So far there are only DFT calculations of single point defect interaction with solute atom in W
M. Muzyk, DNM, K. Kurzydlowski,
N. Baluc, S.L. Dudarev, PRB, 84 (2011) 041115;
T. Suzudo et.al., MSMSE, 22 (2014) 075006
WPMATMethods: A complex interatomic interaction from cluster expansion
formalism for multi-component alloys including vacancies
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Slide 47
Fe-Cr-Ni: J.S. Wrobel, DNM, MY. Lavrentiev, M.Muzyk, S.L. Dudarev, PRB 91, (2015) 024108 (31)
WPMATApplication for W-Re-vacancy systems
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Slide 48
• DFT data base for W-vac systems as discussed
• DFT data base for bcc W-Re
• Focusing on new Re-vac (clusters, voids) data base in bcc-W
WPMAT
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Slide 49
WPMATW-Re-vac: Effective cluster interactions
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Slide 50
• More than 300 DFT energy configurations have been used
• Mapping into CE Hamiltonian gives a very good cross-validation value of 5.3 meV
• Pair and triple clusters are dominant
WPMAT
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Slide 51
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Results at T=2500K: dissociation of Re-vac clusters
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Slide 52
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MC simulations vs. APT
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Slide 53
At higher
T, there is
a smaller
number
of larger
Re-Vac
clusters
2.5 nm
573 K
773 K
WPMAT
Re-Vac clusters from atomic-level analysis
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Slide 54
WPMAT
� For the stage 1, DFT prediction of recovery of SIA & vacancy
recombination is in good agreement with experimental data (U low)
� DFT prediction of He trapping noble-gas impurities is also in excellent
agreement with the TDS measurements. U remains for trapping of He
clusters
� DFT allows to evaluate U from lattice swelling and modulus changes
� Surface-corrected DFT and inter-atomic potential produce a new insight
for vacancy nano-cluster treatments in Stage IV. Systematic KMC
prediction of characteristic temperature of nano-cluster vacancy
dissociation corresponds with the temperature range of SIA dislocation
loop loos. U can be evaluated from hierarchy of multi-scale modelling
� Hybrid DFT/CE/MC method has been generated for alloy with for W-Re-
vacancy systems in order to explain experimental observation of
anomalous Re-cluster precipitation under self-ion irradiation in W alloys.
It opens a way to evaluate U for driven multi-component alloys
Conclusions
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Slide 55
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